# C856 — Resolve retained-zero cases without changing the operation

## Question

Do Adam and Jacob follow the same register model?

## Inputs

```json
{}
```

## Sources

```json
[
  "C852; latest File52c placeholder rule"
]
```

## Opened utc

2026-09-28T02:37:06.899478+00:00

## Results

```json
{
  "retained_zero_cases": [
    {
      "name": "Adam / Creation",
      "n": 410,
      "source_durations": [
        4100,
        2700
      ],
      "placeholder_counts": [
        2,
        2
      ],
      "endpoints": [
        1406,
        8606
      ],
      "delta": 7200
    },
    {
      "name": "Jacob",
      "n": 200,
      "source_durations": [
        2000,
        600
      ],
      "placeholder_counts": [
        3,
        2
      ],
      "endpoints": [
        2006,
        2006
      ],
      "delta": 0
    }
  ],
  "complete_case_partition": [
    14,
    16,
    2
  ]
}
```

## Finding

Adam’s two-placeholders route gives7200 separation; Jacob’s fully retained2000/600 values give0. The exceptional-looking rows are ordinary cases of the stated zero-place rule.

## Reassessment

Test the full paired-field law and rule out one affine column conversion.

## Checks

```json
{
  "complete": true,
  "cases": true,
  "deltas": true
}
```

## Closed utc

2026-09-28T02:37:06.899899+00:00

## Record provenance

Exact record hash: `58887d72b25d05f7b9fe371da97580cc3e822c24cf41f77d75267c943b90e16b`

Source journal: `Research_Cycles/C0832_C0931/journal.json`